Find the value of "k" such that 1/2 is a root of 2x^2+11x=-k

The value of k is -6Step-by-step explanation:The general form of the quadratic equation is y = ax² + bx + cThe roots of the equation is the values of x when y = 0ax² + bx + c = 0, is used to find the roots ∵ 2x² + 11x = -k- Add k to both sides∴ 2x² + 11x + k = 0∵ The roots of the quadratic equations is the values of x when y = 0∵ [tex]\frac{1}{2}[/tex] is a root of the equation- Substitute x by [tex]\frac{1}{2}[/tex] in the equation above to find k∵ 2( [tex]\frac{1}{2}[/tex] )² + 11( [tex]\frac{1}{2}[/tex] ) + k = 0∴ 2( [tex]\frac{1}{4}[/tex] ) + [tex]\frac{11}{2}[/tex] + k = 0∴ [tex]\frac{1}{2}[/tex] + [tex]\frac{11}{2}[/tex] + k = 0- Add the like terms∵ [tex]\frac{1}{2}[/tex] + [tex]\frac{11}{2}[/tex] = [tex]\frac{12}{2}[/tex] = 6∴ 6 + k = 0- Subtract 6 from both sides∴ k = -6The value of k is -6Learn more:You can learn more about the quadratic equations in brainly.com/question/8196933#LearnwithBrainly